Abstract In the framework of the theory of mixture, the dynamic behaviour of solid cylinder bundles submitted to external hydrodynamic load exerted by surrounding viscous fluid flow is described. Mass conservation and momentum balance formulated on an elementary domain made of a given volume of mixture give rise to a system of coupled equations governing solid space-averaged displacement, fluid velocity and pressure provided that near-wall hydrodynamic load on each vibrating cylinder is expressed as a function of both fluid and solid space-averaged velocity fields. Then, the ability of the macroscopic model to reproduce over time an averaged flow surrounding vibrating cylinders in a large array in the context of small magnitude displacements is pointed out. Numerical solutions obtained on a two-dimensional configuration involving an array of several hundreds of cylinders subjected to an impulsional load are compared to those provided by averaged well-resolved microscopic-scale solutions. The relative error is less than 3% in terms of displacement magnitude and 5% for frequency delay. The proposed macroscopic model does not include any assumption on relative effect contributions to mechanical exchanges occurring in the full domain. Therefore it features interesting properties in terms of fluid solid interaction prediction capabilities. Moreover it contributes to a significant gain in terms of computational time and resources. Further developments are now required in order to extent the formulation to large magnitude displacements including three-dimensional effects. This could be recommended for investigations on fuel assembly vibration risk assessment in Pressure Water, Fast Breeder reactors at a whole core scale or any other large-scale mechanical system involving some kind of periodic geometry.

中文翻译：

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基于混合物理论的圆柱排列流固耦合宏观模型

摘要 在混合理论的框架内，描述了固体圆柱束在周围粘性流体流动所施加的外部流体动力载荷下的动力学行为。在由给定体积的混合物组成的基本域上制定的质量守恒和动量平衡产生了一个耦合方程系统，该方程组控制固体空间平均位移、流体速度和压力，前提是每个振动圆柱体上的近壁流体动力载荷表示为流体和固体空间平均速度场的函数。然后，指出了宏观模型在小幅位移的情况下随着时间的推移再现围绕大阵列振动圆柱体的平均流动的能力。将在二维配置上获得的数值解与由平均分辨率良好的微观解提供的解进行比较，该二维配置涉及数百个圆柱体的阵列，它们受到冲击载荷。位移幅度的相对误差小于 3%，频率延迟的相对误差小于 5%。所提出的宏观模型不包括对发生在整个域中的机械交换的相对影响贡献的任何假设。因此，它在流固相互作用预测能力方面具有有趣的特性。此外，它有助于显着增加计算时间和资源。现在需要进一步的发展，以便将公式扩展到包括三维效应在内的大位移。